Prior art includes a large body of published work relating to the shaping of femtosecond pulses and the interactions between various materials or molecules with the shaped pulses. It has been observed that in nonlinear systems such as molecules and semiconductor materials, intense light pulses of certain shapes can be used to enhance the fluorescent emission at particular wavelengths. The specific pulse shape needed depends on the complex energy band structure of the molecules or materials being studied. In principle, a detailed and precise understanding of the physics involved should be enough to calculate the optimal pulse shape, but in practice our understanding is insufficient and our computational tools are too crude to do the calculations.
In “Feedback quantum control of population transfer using shaped femtosecond pulses”, published in Ultrafast Phenomena XI, 1998, K. R. Wilson and his associates demonstrated a method for evolving an optimal pulse shape to control the quantum state of a complex molecular system. The method is illustrated in FIG. 1. A very brief light pulse is spread into a spectrum by a diffraction grating, then the spectrum is passed through a spatial light modulator that modulates each spectral component independently. The modulator can operate on phase, amplitude or both. Typical spatial light modulators used for pulse shaping are acousto-optic modulators, liquid crystal modulators and deformable-mirror arrays. The pulse is then reconstituted by focusing the modulated spectral components back to a point on a diffraction grating, which combines the components coherently into a single pulse. In essence, the spatial light modulator acts on the temporal Fourier transform of the initial pulse to re-form it in any way desired.
A substance such as a particular protein responds nonlinearly to a pulse of light. For example, an ultraviolet light pulse a few tens of femtoseconds long will induce fluorescence in most substances; and the spectrum of the fluorescence depends on the intensity of the pulse. If the intensity is great enough, there is an increased probability of multiphoton absorption resulting in electrons being elevated to energy levels higher than the energy of a single photon, which leads to emission at wavelengths that single-photon absorption cannot produce.
In addition to intensity, the spectral content of a light pulse and the relative phase and polarization of the spectral components can affect strongly the response of an illuminated sample. For example, it has been shown by Bardeen et al (Ref. 1) that when a laser light pulse is shaped appropriately, the intensity of a fluorescence emission line from an irradiated sample can be much higher than it is with an arbitrarily shaped pulse. That is, the ratio of the intensity of a specific emission line to the intensity of another specific emission line can be maximized by using an optimally-shaped pulse.
The importance of pulse shape to the response of a nonlinear system like an atom can be understood by considering a double pendulum stimulated by a short series of impacts. If a series of impacts strike the pendulum at times separated by a time equal to the period of the fundamental mode of the pendulum, the pendulum will respond by swinging without wiggling. If, however, the impacts are timed so that some are synchronous with the fundamental mode, but other impacts are interspersed with the first impacts so that the other impacts are synchronous with the vibrational period of the upper mass, the pendulum will respond by both swinging and wiggling. In the case of a quantum mechanical system like a molecule, a properly shaped pulse can elevate electrons to a specific energy level and then give them a second “kick” to elevate them further to another energy level that is otherwise not easily accessible. Decay from that energy level to other energy levels en route to the ground state, then, produces emission lines that will only be present when the excitation pulse has precisely the shape required to provide the first “kick” followed by a properly timed second “kick”. Furthermore, the direction of the electric fields in a pulse during the first and second “kicks” is important because the vibratory state or quantum state of an electron in a molecule or atom has a directional component. So, in an optimal pulse, the polarization state of the light may need to change once or even several times within the pulse duration in order to elevate the illuminated substance to a desired quantum state.
In the prior art, femtosecond laser pulses have been shaped by forming their temporal Fourier transform, manipulating individual Fourier components independently in both phase and amplitude, and then forming the inverse Fourier transform. This is accomplished as illustrated in FIG. 1, by forming the dispersed spectrum of an original pulse 153 using a diffraction grating 130, passing the spread spectrum through a spatial light modulator 105, 110 (such as a liquid crystal light valve or an acousto-optic light modulator) to selectively attenuate and/or delay various portions of the spectrum, and then focusing the spectrum back together onto a second diffraction grating 100, where the pulse is re-formed, producing a pulse having a modified shape.
Also in the prior art, the optimum pulse shape is determined empirically by monitoring the emission spectrum of a sample irradiated by the shaped pulse and adjusting the shape until the emission spectrum is optimized. For example, if the spatial light modulator 105, 110 is a liquid crystal light modulator, the pixels of the modulator can be treated as “genes” while the height of a specific emission line can be treated as “fitness” in a genetic algorithm or other evolutionary algorithm.
The basic techniques of laser pulse shaping and pulse shape optimization have been explored by many researchers, with the purpose of performing measurements on molecular dynamics, generating x-rays, and controlling chemical reactions.